A small sphere having a diameter of 6 mm has an electrical coil inside, which ma

Question

A small sphere having a diameter of 6 mm has an electrical coil inside, which maintains the outer surface temperature at 220C. The sphere is exposed to an air stream at 1 atm and 20C with a velocity of 20 m/s. Calculate the heating rate (W) that must be supplied to the sphere. Note the following. For air, the requirement for the Whitaker correlation on the dynamic viscosity ratio appears to be slightly out of range, but go ahead and compute this with as the 'error' is very small (note the 0.25 exponent). Actually, the original paper states that the data scatter around the correlation is 30%, which is entirely reasonable. In this correlation, properties are evaluated at Tinf except the viscosity at the sphere wall. Another possibility for spheres is the McAdams correlation Nu=0.37*Re**0.6 17

Explanation / Answer

taking Nu=0.37*Re^0.6

air: kinematic viscosity (Y)=15.11*10^-6

k=0.0257

hd/k=0.37*(vd/Y)^0.6

h=346.7 w/m2.k

A=pie*(0.003)^2=2.83*10^-5 m2

q=h.A.(T1-T2)

=346.7*A*(220-20)=1.962322 W

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